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Math Help - dice

  1. #1
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    dice

    Can you help me with a dice probability problem?
    If there are 3 standard die which are numbered as follows:

    die A - 1,2,3,4,5, and one blank face
    die B - 5,6,7, and 3 blank faces
    die C - 7,8 and four blank faces

    If the highest number was the winning throw which die is the most likely winner?
    If A,B and C were all thrown? or If A and B only were thrown, A and C or if B and C only were thrown?
    Last edited by snowman; November 4th 2008 at 06:30 AM. Reason: spelling
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  2. #2
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    Quote Originally Posted by snowman View Post
    Can you help me with a dice probability problem?
    If there are 3 standard die which are numbered as follows:

    die A - 1,2,3,4,5, and one blank face
    die B - 5,6,7, and 3 blank faces
    die C - 7,8 and four blank faces

    If the highest number was the winning throw which die is the most likely winner?
    If A,B and C were all thrown? or If A and B only were thrown, A and C or if B and C only were thrown?
    The way you have phrased this makes it hard to understand. This is my guess at what you were trying to ask.

    If A, B, and C were all thrown, obviously C is more likely to have the highest number- A can be no higher than 6, B no higher than 7 while C is no lower than 7.

    If "A and C" or "B and C" are thrown, the answer is still obviously C.

    If "A and B" are thrown, the expected value for A is (1+ 2+ 3+ 4+ 5)/6= 2.5 while the expected value for B is (5+ 6+ 7)/6= 3. B is more likely to have the higher number.
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  3. #3
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    There are indeed several problems with that wording.
    What happens in the case of the dice showing the same outcome?
    B & C could both be 7, in that case is there a winner?
    All three could be blank. Then what?
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  4. #4
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    Sorry that my wording is a bit wooly and confusing.
    I will try to simplify the question .
    The dice are numbered:

    Die A - 1, 2, 3, 4, 5 and one blank face
    Die B - 5, 6, 7 and three blank faces
    Die C - 7, 8 and four blank faces

    Give there are three people and three dice -
    Which die would you choose to give the greatest chance of rolling a winning number ( highest number wins, in the event of a tie die are rolled again until there is a winner )
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  5. #5
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    If A is against B: B wins \frac{17}{36} and A wins \frac{15}{36}.

    If A is against C: A wins \frac{20}{36} and C wins \frac{12}{36}.

    If C is against B: B wins \frac{12}{36} and C wins \frac{11}{36}.

    I don't know if that is what you mean.
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  6. #6
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    Quote Originally Posted by snowman View Post
    Can you help me with a dice probability problem?
    If there are 3 standard die which are numbered as follows:

    die A - 1,2,3,4,5, and one blank face
    die B - 5,6,7, and 3 blank faces
    die C - 7,8 and four blank faces

    If the highest number was the winning throw which die is the most likely winner?
    If A,B and C were all thrown? or If A and B only were thrown, A and C or if B and C only were thrown?
    Hi Snowman,

    I'm assuming a blank face effectively counts as a zero.

    I'll take the first case, where all three players throw.

    A wins only if B and C both roll blanks and A rolls a non-blank. So P(A wins) = (3/6) * (4/6) * (5/6) = 0.09259.

    B wins if C rolls a blank and B rolls a non-blank, except for the case where A and B both roll 5s. So P(B wins) = (4/6) * [(3/6) - (1/6) * (1/6)] = 0.3148.

    C wins if C rolls an 8, or if C rolls a 7 and B rolls a non-7. So P(C wins) = 1/6 + (1/6) * (5/6) = 0.3056.

    So B has the greatest probability of winning.
    Last edited by awkward; November 4th 2008 at 02:28 PM. Reason: corrected typo
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